What is the difference between a Music Tie and a Slur?
The curved line connecting the heads of two notes of the same pitch is called a tie and indicates that the two notes must be played as a single note with the same duration as the sum of the individual notes.
The following illustrates a tie

You might tie two notes which could be written with a single note value, such as a quarter note tied to an eighth note (the same length as a dotted quarter). One example of when you would use a tie is because a barline is in between the notes.
A tie is similar in appearance to a slur.
A slur in piano music is two or more notes played together, one right after the other, in a smooth fashion. A slur marking, indicated by a curved line that begins at the first note of the slur and ends at the last
The following illustrates a slur



